Conservative groups and lawmakers are lining up against a proposal by Senate Republicans to impose automatic tax increases on millions of Americans — if their sweeping tax package doesn't grow the economy and raise tax revenues as much as projected.

The opposition comes as the tax package cleared a key procedural vote in the Senate on Wednesday. The Senate voted 52-48 to start debating the bill. Wednesday's vote potentially could pave the way for the Senate to pass the package later this week. The Senate could start voting on amendments Thursday evening.

Opposition to the tax "trigger" could doom a delicately negotiated proposal aimed at mollifying deficit hawks who worry that tax cuts for businesses and individuals could add trillions to the mounting national debt.

Tucking a potential tax increase into the tax cut bill isn't sitting well with conservatives.

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"Automatic tax increases are a special level of insanity," said Rep. Trent Franks, R-Ariz. "I don't think it survives."

Rep. Jeb Hensarling, R-Texas, called the proposal "a uniquely bad idea," especially if revenues fall short because of an unforeseen slowdown in the economy.

Rep. Mark Sanford, R-S.C., said the threat of an automatic tax increase would make businesses reluctant to invest.

"If businesses or individuals have no ability to plan on a rate, it makes an investment decision, for instance, very, very difficult," Sanford said.

The proposal is being pushed by Republican Sens. Bob Corker of Tennessee, James Lankford of Oklahoma and Jeff Flake of Arizona. It is picking up steam in the GOP-controlled Senate, even if it could land with a thud in the GOP-controlled House.

Corker said he has received assurances from Republican Senate leaders and the White House that some sort of "trigger" would be added to the Senate package that would increase taxes if the economy doesn't grow — and tax revenues don't increase — as much as projected.

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"While we are still working to finalize the details, I am encouraged by our discussions," Corker said.

Senators are also considering a companion proposal from Sen. Ted Cruz, R-Texas, that would automatically cut taxes further if the economy grows faster than expected.

The overall package is a blend of generous tax cuts for businesses and more modest tax cuts for families and individuals. It would mark the first time in 31 years that Congress has overhauled the tax code, making it the biggest legislative achievement of President Donald Trump's first year in office.

In crafting the bill, Senate Majority Leader Mitch McConnell, R-Ky., has been trying to balance sometimes competing interests with very little room for error. Sen. Steve Daines, R-Mont., said Wednesday he would support the bill after reaching a deal to sweeten tax cuts for business owners who report their business income on their individual tax returns.

Senate Republicans hold a slim 52-48 majority in the Senate, meaning they can only lose two votes, with Vice President Mike Pence casting the tie-breaker.

Pence was dining Wednesday night with a group of Republican senators, some of whom have expressed reservations about the tax bill. Pence invited Flake, Daines, Lankford and David Perdue of Georgia to the vice president's residence to discuss the tax overhaul, budget and other priorities, the White House said.

Sen. Dean Heller, R-Nev., said, "Personally I prefer not to have a trigger, but I wouldn't vote against the bill. We'll do what we can do to get Bob Corker's vote."

An estimate by congressional analysts says the Senate tax bill would add $1.4 trillion to the budget deficit over the next decade. GOP leaders dispute the projection, saying tax cuts will spur economic growth, reducing the hit on the deficit.

Many economists disagree with such optimistic projections. The trigger would be a way for senators to test their economic assumptions, with real consequences if they are wrong.

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A number of conservative groups that are usually allied with Republicans are slamming the idea.

The U.S. Chamber of Commerce issued a statement calling the trigger "impractical, unreasonable, and unnecessary."